Regioselective acylation of aminoresorcinarenes

The acid catalyzed hydrolytic cleavage of the oxazine rings in the readily available tetraoxazine derivatives of resorcinarenes results in tetraaminoresorcinarenes. A similar process applied to C₂-symmetrical bisoxazine resorcinarene tetratosylates affords C_2v-symmetrical resorcinarenediamines. The mild acylation of these resorcinareneamines with BOC-anhydride or para-nitrophenyl ester proceeds selectively at the nitrogen atoms without affecting the hydroxyl groups. Most of the resulting resorcinareneamides are thus obtained in preparative yields and can be easily purified by simple crystallizations. In the crystalline state the compounds obtained are found to bind chloride anions through hydrogen bonds and electrostatic interactions and to display a chiral arrangement of hydrogen bonded functional groups at the wide rim of the macrocycle.     

Solution of linear equations with Hankel and Toeplitz matrices

Summary An algorithm is described for solving a linear equationA x=c, whereA is ann×n Hankel or Toeplitz matrix, inO (n ²) arithmetic operations. As contrasted with earlier such algorithms the present one does not require the principal minors ofA to be non-zero except detA.     

Photodissociation of formyl fluoride in rare gas matrixes

Photodissociation of formyl fluoride (HCOF) is studied in Ar, Kr, and Xe matrixes at 248 and 193 nm excitation by following spectral changes in the infrared absorption spectra. In all matrixes, the main photodissociation products are CO/HF species, including CO-HF and OC-HF complexes and thermally unstable CO/HF species (a distorted CO/HF complex or a reaction intermediate), which indicate negligible cage exit of atoms produced via the C-F and C-H bond cleavage channels. However, the observation of traces of H, F, CO, CO(2), F(2)CO, FCO, and HRg(2)(+) (Rg = Kr or Xe) in Kr and Xe matrixes would imply some importance of other reaction channels too. The analysis of the decay curves of the precursor shows that dissociation efficiency of HCOF increases as Ar < Kr < Xe, the difference being the factor of 10 between Ar and Xe. Moreover, HCOF dissociates 20-50 times faster at 193 nm compared to 248 nm. Interestingly, whereas the CO/HF species are stable with respect to photolysis in Ar, they photobleach in Kr and Xe matrixes at 248 and 193 nm, even though the first excited states of CO and HF are not energetically accessible with 193 and 248 nm photons. In krypton matrix, the photodissociation of CO/HF species at 248 nm is observed to be a single photon process. Quantum chemical calculations of electronic excitation energies of CO-HF and OC-HF complexes show that the electronic states of HF and CO mostly retain their diatomic nature in the pair. This clearly demonstrates that photodissociation of CO/HF complexes is promoted by the surrounding rare gas lattice.     

Model selection by sequentially normalized least squares

Model selection by means of the predictive least squares (PLS) principle has been thoroughly studied in the context of regression model selection and autoregressive (AR) model order estimation. We introduce a new criterion based on sequentially minimized squared deviations, which are smaller than both the usual least squares and the squared prediction errors used in PLS. We also prove that our criterion has a probabilistic interpretation as a model which is asymptotically optimal within the given class of distributions by reaching the lower bound on the logarithmic prediction errors, given by the so called stochastic complexity, and approximated by BIC. This holds when the regressor (design) matrix is non-random or determined by the observed data as in AR models. The advantages of the criterion include the fact that it can be evaluated efficiently and exactly, without asymptotic approximations, and importantly, there are no adjustable hyper-parameters, which makes it applicable to both small and large amounts of data.     

High Accuracy Protein Structures from Minimal Sparse Paramagnetic Solid‐State NMR Restraints

There is a pressing need for new computational tools to integrate data from diverse experimental approaches in structural biology. We present a strategy that combines sparse paramagnetic solid‐state NMR restraints with physics‐based atomistic simulations. Our approach explicitly accounts for uncertainty in the interpretation of experimental data through the use of a semi‐quantitative mapping between the data and the restraint energy that is calibrated by extensive simulations. We apply our approach to solid‐state NMR data for the model protein GB1 labeled with Cu²⁺‐EDTA at six different sites. We are able to determine the structure to 0.9 Å accuracy within a single day of computation on a GPU cluster. We further show that in some cases, the data from only a single paramagnetic tag are sufficient for accurate folding.     

Subcomponent Self-Assembly of a Cyclic Tetranuclear FeII Helicate in a Highly Diastereoselective Self-Sorting Manner

An enantiomerically pure diamine based on the 4,15-difunctionalized [2.2]paracyclophane scaffold and 2-formylpyridine self-assemble into an optically pure cyclic metallosupramolecular Fe₄L₆ helicate upon mixing with iron(II) ions in a diastereoselective subcomponent self-assembly process. The cyclic assembly results from steric strain that prevents the formation of a smaller linear dinuclear triple-stranded helicate, and hence, leads to the larger strain-free assembly that fulfils the maximum occupancy rule. Interestingly, use of the racemic diamine also leads to a racemic mixture of the homochiral cyclic helicates as the major product in a highly diastereoselective narcissistic chiral self-sorting manner given the fact that the assembly contains ten stereogenic elements, which can in principle give rise to 149 different diastereomers. The metallosupramolecular aggregates could be characterized by NMR, UV/Vis and CD spectroscopy, mass spectrometry, and X-ray crystallography.